Indicator smoothing: lookback, weight, and scale

Replacing a noisy series

A noisy indicator series is commonly damped by replacing the raw values with a simple moving average or an exponential average. A moving average is a trailing mean over a fixed number of ordered observations, rebuilt by dropping the oldest point when a new one arrives. A simple moving average of a chosen length is the mean of that many most recent observations and, at the next sample, is recomputed by deleting the oldest observation and inserting the newest.

Lookback sets smoothness and delay

Lookback is the sampling length that jointly sets smoothness and how stale the average is. Smoothing strength rises with lookback length: a five-week average is described as moderately smooth, while a 52-week average is described as highly subdued. Length is chosen by balancing extra smoothness against extra delay.

Where the average is plotted

Centering is placing a window average at the midpoint of the observations it contains rather than on the latest sample. A moving average belongs at the center of its window because each included point has equal weight, yet market charts usually attach it to the most recent observation. A centered average is out of date by half its length, so a two-week average lags by one week and a 52-week average lags by 26 weeks.

Exponential updates and a short start

Exponential smoothing is a recursive mix of the prior smoothed value and the newest observation using two complementary percentages. An exponential average updates by multiplying the prior exponential value by one percentage and the newest observation by a complementary percentage that together equal 100, which both eases calculation and tilts weight toward recent data.

If no prior exponential value exists, a short simple average of the first observations can initialize the recursion, and the earliest exponential values should be treated as provisional.

To approximate a simple average of period A, the newest observation receives weight 200/(A+1) percent and the prior exponential receives the remainder. For A equal to 5 the split is 33.33 and 66.67, and for A equal to 52 it is 3.8 and 96.2.

Integer weights as another recency tilt

A weighted moving average is a window average that multiplies nearer observations by larger integer weights before averaging the products. It can assign descending integers such as 9, 8, and 7 to successively older observations, then average the products, producing a recency bias that an exponential average also supplies with simpler arithmetic.

Arithmetic and logarithmic scale

When an indicator rises to a much higher level, an arithmetic scale can magnify later swings. A logarithmic scale, or converting the series to logarithms and plotting those values on an arithmetic axis, restates the swings in percentage terms.